SHARP HIGH-FREQUENCY ESTIMATES FOR THE HELMHOLTZ EQUATION AND APPLICATIONS TO BOUNDARY INTEGRAL EQUATIONS

被引：43

作者：

Baskin, Dean ^{[1
]}

Spence, Euan A. ^{[2
]}

Wunsch, Jared ^{[3
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[3] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2016年 / 48卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Helmholtz equation; high frequency; boundary integral equation; scattering theory; NUMBER-EXPLICIT BOUNDS; WAVE-EQUATION; SCATTERING; OPERATORS; SINGULARITIES; STABILITY; DECAY; APPROXIMATION; STABILIZATION; RESONANCES;

D O I：

10.1137/15M102530X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider three problems for the Helmholtz equation in interior and exterior domains in R-d (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for exterior Helmholtz problems.

引用

页码：229 / 267

页数：39

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